Locally symmetric areas are generalizations of areas of continuing curvature. during this booklet the writer offers the facts of a amazing phenomenon, which he calls "strong rigidity": this can be a improved kind of the deformation tension that has been investigated by way of Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan.
The facts combines the idea of semi-simple Lie teams, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian areas, components of ergodic concept, and the basic theorem of projective geometry as utilized to Tit's geometries. In his evidence the writer introduces new notions having self sufficient curiosity: one is "pseudo-isometries"; the opposite is a suggestion of a quasi-conformal mapping over the department algebra ok (K equals actual, advanced, quaternion, or Cayley numbers). the writer makes an attempt to make the account available to readers with diversified backgrounds, and the e-book includes pill descriptions of many of the theories that input the proof.
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